If a triangle has side lengths 16, 11, and 10, what kind of triangle is it and how do you find that out?

what you are hoping for is that it is a right triangle. Use Pythagoras formula.
\[c^2 = a^2+ b^2\]
where c is the longest side. IF you get a true statement out of this then your triangle is a right triangle.
\[16^2 = 10^2 + 11 ^2\]?
\[256 = 100 + 121\]?
\[256 = 221\]?
no, 256 does not equal 221, so in this case it is not a right triangle

if
\[c^2 < a^2 + b^2\]
then you have an acute triangle, meaning that all the angles are smaller than 90 degrees.
if
\[c^2 > a^2 + b^2\]
then you have an obtuse triangle, meaning that 1 angle of the triangle is greater than 90 degrees.
in this case,
\[c^2 > a^2 + b^2\]
so you have an obtuse triangle